Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
264 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3⋊#859 | C2 | direct (N × H) |
| 6. C2×C3×SL(2,𝔽3) | C4 | semidirect |
| 18. C3×SL(2,𝔽3) | C2×C4 | semidirect |
| 22. C2×C3×Q8 | Dic3 | semidirect |
| 27. C2×SL(2,𝔽3) | Dic3 | semidirect |
| 48. C3×Q8 | C2×Dic3 | semidirect |
| 57. SL(2,𝔽3) | C2×Dic3 | semidirect |
| 65. C2×Q8 | C3⋊Dic3 | semidirect |
| 91. Q8 | C2×C3⋊Dic3 | semidirect |
| 103. C2×C3 | #859 | semidirect |
| 116. C3 | C2×#859 | semidirect |
| 117. C2 | C3⋊#859 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×SL(2,𝔽3) | 2 |
| C3⋊#859 | 2 |
| C2×#859 | 3 |
| C2×#835 | 3 |
| C22×C3⋊Dic3 | 4 |